Count ordered distinct selections, repeated strings and fixed-multiplicity arrangements with exact integer arithmetic.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
Distinct selections: P(n,r)=n!/(n−r)!. Repeated ordered strings: nʳ. Multiset arrangements: (Σc)!/∏c!.
Assumptions and limits
Exact integer counts. Ordered positions matter. In multiset mode, identical copies within each type are indistinguishable. Eligibility restrictions, circular equivalence and forbidden adjacency are not modeled.
Worked example
For ten distinct objects in three ordered positions, the count is 720. Repetition permits 1,000 strings. Multiset counts 2,2,1 instead describe 30 full arrangements.
Worked reading and practical questions
- Count Ranked Shortlists and Top-r Finishes without Ties
- Arrange Repeated Items Without Counting Identical Swaps
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
Exact integer counts. Ordered positions matter. In multiset mode, identical copies within each type are indistinguishable. Eligibility restrictions, circular equivalence and forbidden adjacency are not modeled.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.